Just clip the nails unless it's torn back at the quick. If that's the case have your vet do it. You should always have quick stop (styptic/antiseptic powder) or similar around both for nail clipping and the occasional break. If it's bleeding pretty badly you may need your vet.
Is the claw really split or is the outside sheath just being shed? If it's just shedding, just kind of pull and peel. That's what happens when a cat 'sharpens' it's claws, peeling off that outer sheath. If it IS split and not bleeding, stabilize the split with a dab of 'Crazy Glue'. Make sure not to let your cat get a whiff of the glue. If you do and your cat starts frothing, at the mouth and drooling, don't worry too much. I had a big Main Coon who scratched, before I learned who to trim claws and I'd glue little glass beads (cheaper than the 'Velvet Claws' product) with big holes to the very tips, Sometimes my cat would do that, but didn't seem any worse for wear for it. If it's a really bad split, don't use the glue and see your vet right away
